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Babinet’s principle for elastic waves: A numerical test

By
José M. Carcione
José M. Carcione
Osservatorio Geofisico Sperimentale, P.O. Box 2011 Opicina, 34016 Trieste, Italy Electronic mail: carcione@gems755.ogs.trieste.it
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Anthony F. Gangi
Anthony F. Gangi
Department of Geology and Geophysics, Texas A&M University, College Station, Texas 77843-3114 Electronic mail: gangi@tamu.edu
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Published:
January 01, 2016

Abstract

Babinet’s principle states that the diffracted fields from complementary screens are the negative of each other. In electromagnetics, Babinet’s principle for infinitely thin perfectly conducting complementary screens implies that the sum, beyond the screen plane, of the electric and the magnetic fields (adjusting physical dimensions) equals the incident (unscreened) electric field. A test of the principle for the elastodynamic case was made using numerical calculations, and the results demonstrate that Babinet’s principle holds quite well for complementary plane screens with contrasting boundary conditions; that is, the complementary screen of a stress-free screen is a rigid screen with openings where the original stress-free screen existed, and vice versa. The results are exact in an anisotropic SH case; for the P-SV case, the diffracted waves, PdP, SdS, PdS, and SdP satisfy the principle exactly, while the refracted waves, PdPrSc and SdPrSc, do not satisfy the principle at all (these waves are generally much smaller than the PdS and SdP waves). Diffracted surface waves also do not satisfy the principle. The numerical method is based on a domain-decomposition technique that assigns a different mesh to each side of the screen plane. The effects of the screens on wave propagation are modeled through the boundary conditions, requiring a special boundary treatment based on characteristic variables. The algorithm solves the velocity/ stress wave equations and is based on a Fourier/Chebyshev differential operator. © 1999 Acoustical Society of America. [S0001-4966(99)01403-4]

PACS numbers: 43.20.Bi, 43.20.Gp, 43.20.Px [DEC]

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Society of Exploration Geophysicists Geophysics Reprint Series

Seismic Diffraction

Kamil Klem-Musatov
Kamil Klem-Musatov
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Henning Hoeber
Henning Hoeber
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Michael Pelissier
Michael Pelissier
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Tijmen Jan Moser
Tijmen Jan Moser
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Society of Exploration Geophysicists
Volume
30
ISBN electronic:
9781560803188
Publication date:
January 01, 2016

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